By Madisetti V. (ed.)
ISBN-10: 1420046063
ISBN-13: 9781420046069
Now to be had in a three-volume set, this up-to-date and elevated variation of the bestselling The electronic sign Processing guide keeps to supply the engineering neighborhood with authoritative assurance of the basic and really expert facets of information-bearing signs in electronic shape. Encompassing crucial historical past fabric, technical information, criteria, and software program, the second one variation displays state-of-the-art info on sign processing algorithms and protocols with regards to speech, audio, multimedia, and video processing expertise linked to criteria starting from WiMax to MP3 audio, low-power/high-performance DSPs, colour photo processing, and chips on video. Drawing at the adventure of prime engineers, researchers, and students, the three-volume set includes 29 new chapters that handle multimedia and web applied sciences, tomography, radar structures, structure, criteria, and destiny functions in speech, acoustics, video, radar, and telecommunications. Emphasizing theoretical recommendations, electronic sign Processing basics offers entire assurance of the fundamental foundations of DSP and contains the next elements: signs and platforms; sign illustration and Quantization; Fourier Transforms; electronic Filtering; Statistical sign Processing; Adaptive Filtering; Inverse difficulties and sign Reconstruction; and Time–Frequency and Multirate sign Processing.
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Additional resources for The digital signal processing fundamentals
Example text
4 Properties of the DTFT Sequence x[n] y[n] Fourier X(e jv ) Y(e jv ) 1. ax[n] þ by[n] aX(e jv ) þ bY(e jv ) 2. x[n À nd ] eÀjvnd X(e jv )  à X e jðvÀv0 Þ 3. e jv0 n (nd an integer) x[n] X(eÀjv ) 4. x[Àn] if x[n] real X*(e jv ) dX(e jv ) dv 5. nx[n] j 6. x[n] ¼ y[n] X(e jv )Y(e jv )  à Ðx 1 X(e ju )Y e j(vÀu) du 2p 7. x[n]y[n] Àx Parseval’s theorem 1 Ðx P 1 jx[n]j2 ¼ 2p jX(e jv )j2 dv 8. 9. V. , Discrete-Time Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1989. With permission. Digital Signal Processing Fundamentals 1-14 operation, F À1 fÁg denotes the inverse DTFT operation, and ‘‘*’’ denotes the DT convolution operation defined as f1 [n] * f2 [n] ¼ þ1 X f1 [n]f2 [n À k]: k¼À1 1.
For example, Property 5 (time-shifting property), holds for circular shifts of the finite length sequence s[n], which is consistent with the notion that the DFT treats s[n] as one period of a periodic sequence. Also, the multiplication of two DFTs results in the circular convolution of the corresponding DT sequences, as specified by Property 7. This later property is quite different from the linear convolution property of the DTFT. 5 Properties of the DFT Finite-Length Sequence (Length N) N-Point DFT (Length N) 1.
We shall deal here only with ordinary differential equations. In the mathematical texts, the independent variable is generally x, which can be anything such as time, distance, velocity, pressure, and so on. In most of the applications in control systems, the independent variable is time. For this reason we shall use here independent variable t for time, although it can stand for any other variable as well. The following equation d2 y dt 2 4 þ3 dy þ 5y2 (t) ¼ sin t dt is an ordinary differential equation of second order because the highest derivative is of the second order.